Mayoral hopeful Christine Quinn yesterday proposed spending $365 million a year and racking up an additional $1.5 billion in debt to pay for a slew of new social programs, as she gears up for this year’s Democratic primary.

In her final State of the City speech as City Council speaker, Quinn pitched a 10-year expansion of affordable-housing programs to create 40,000 units at a cost of $300 million a year.

Her staff said the money would come from a combination of unspent capital funds in the city budget, other savings they claimed to have identified but declined to detail, and borrowing $150 million a year while taking advantage of low interest rates.

Also proposed: $50 million to expand a child-care tax credit to the middle class, although a similar program that Quinn announced last year has yet to get under way, and $13 million to expand the city’s adult-education programs.

Her staff said the council has identified enough budgetary savings to cover the programs’ costs — but they did not rule out a future property-tax hike. Quinn has said she would not support such an increase this year.